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ab+1,bc+1, cd+1, da+1 simultaneously perfect square

Source: Danube 2012 junior p1

July 22, 2019

Perfect SquaresPerfect Squarenumber theory

Problem Statement

a) Exist

a, b, c, \in N

, such that the numbers

ab+1,bc+1

and

ca+1

are simultaneously even perfect squares ? b) Show that there is an infinity of natural numbers (distinct two by two)

a, b, c

and

d

, so that the numbers

ab+1,bc+1, cd+1

and

da+1

are simultaneously perfect squares.